Gurantor department | Department of Applied Mathematics | Credits | 4 |

Subject guarantor | doc. Ing. Dalibor Lukáš, Ph.D. | Subject version guarantor | doc. Ing. Dalibor Lukáš, Ph.D. |

Study level | undergraduate or graduate | Requirement | Optional |

Year | 2 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2015/2016 | Year of cancellation | |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
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Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

The aim of the course is to introduce fundamental numerical methods for solution of engineering problems that lead to large-scale linear systems, nonlinear systems, or eigenvalue problems. Further, we shall present interpolation methods and an approximation by the method of least squares. Finally, we shall focus on numerical derivatives, quadrature, and we introduce methods for solution of boundary value problems for partial diferential equations. Each topic will be motivated by an engineering problem. The algorithms will be implemented in Matlab. The students will be also introduced to some libraries of numerical linear algebra such as BLAS, LAPACK, and MUMPS.

Lectures

Tutorials

The course covers fundamental methods of numerical linear and nonlinear algebra, methods of interpolation and approximation, and numerical analysis including an introduction to solution of boundary value problems for partial differential equations.

- Quarteroni, A. – Sacco, R. – Saleri, F. Numerical Mathematics. Springer, 2000.

- W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes in C. Cambridge University Press, Cambridge 1990.

test, project

Basic knowledge of linear algebra, derivatives, and integrals

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method
Exercises:
1. Numerical linear algebra - iterative methods for solution to linear systems
2. Numerical linear algebra - the method of conjugate gradients, preconditioning
3. Numerical linear algebra - sparse matrix solvers, parallel frontal method
4. Numerical linear algebra - eigenvalues and eigenvectors, power method, Lanczos method
5. Numerical linear algebra - libraries BLAS, LAPACK, MUMPS
6. Nonlinear systems - bisection, fixed-point iterations, Newton's method
7. Interpolation and approximation - Lagrange interpolation, splines, B-splines, approximation by the method of least squares
8. Numerical analysis - numerical derivative, numerical quadrature
9. Numerical analysis - introduction to numerics for partial differential equations
10. Numerical analysis - principle of the finite element method

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points |
---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 |

Credit | Credit | 30 | 10 |

Examination | Examination | 70 | 21 |

Show history

Academic year | Programme | Field of study | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2020/2021 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (2612T025) Computer Science and Technology | K | Czech | Ostrava | 2 | Optional | study plan |

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